Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
438 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #100×D163 | C2 | semidirect |
| 3. #99×D163 | C2 | semidirect |
| 4. #23781453 | C2 | semidirect |
| 5. #23781452 | C2 | semidirect |
| 6. #23781451 | C2 | semidirect |
| 7. AΣL(1,𝔽16)×C163 | C2 | semidirect |
| 8. C24×D163 | C4 | semidirect |
| 13. #19104705 | C4 | semidirect |
| 14. #19104704 | C4 | semidirect |
| 19. C22⋊C4×D163 | C4 | semidirect |
| 20. #19104652 | C22 | semidirect |
| 22. #19104650 | C22 | semidirect |
| 25. #100×C163 | C22 | semidirect |
| 26. #99×C163 | C22 | semidirect |
| 33. C23×D163 | C2×C4 | semidirect |
| 52. C22⋊Dic163 | C2×C4 | semidirect |
| 57. C24×C163 | C2×C4 | semidirect |
| 63. C22⋊C4×C163 | C2×C4 | semidirect |
| 156. D163 | AΣL(1,𝔽16) | direct (N × H) |
| 157. C163 | C2×AΣL(1,𝔽16) | semidirect |
| 165. AΣL(1,𝔽16) | D163 | direct (N × H) |
| 181. #100 | C2×D163 | semidirect |
| 184. #99 | C2×D163 | semidirect |
| 193. C24 | C4×D163 | semidirect |
| 221. C22⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #120×D163 | 2 |
| #100×D163 | 2 |
| #99×D163 | 2 |
| #23781453 | 2 |
| #23781452 | 2 |
| #23781451 | 2 |
| AΣL(1,𝔽16)×C163 | 2 |
| C2×AΣL(1,𝔽16) | 163 |